Vacuum polarization in molecules. I. Uehling interaction

Radiative corrections to electronic structure are characterized by perturbative expansions in $\ensuremath{\alpha}$ and $Z\ensuremath{\alpha}$, where $\ensuremath{\alpha}$ is the fine-structure constant and $Z$ is the nuclear charge. A formulation of the leading-order $\ensuremath{\alpha}(Z\ensuremath{\alpha})$ Uehling contribution to the renormalized vacuum polarization is reported in a form that is convenient for implementation in computational studies of the relativistic electronic structures of molecules. Benchmark calculations based on these methods are reported that include the leading-order vacuum polarization effects within relativistic mean-field methods for the $\mathrm{E}{119}^{+}$ ion and the closed-shell diatomic species E119F.